Question

Two oranges, three bananas and four apples cost Rs. 15. Three oranges, two bananas and one apple cost Rs. 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay ?

• A. Rs.10
• B. Rs.8
• C. Rs.15
• D. Cannot be determined

Answer 1

The Correct Option is C

To solve this problem, we need to set up equations based on the information given and then determine the total cost for purchasing the given fruits.

Step 1: Setup the equations

We have the following two scenarios:

• Two oranges, three bananas, and four apples cost Rs. 15.
• Three oranges, two bananas, and one apple cost Rs. 10.

Let's denote:

• The cost of one orange as x.
• The cost of one banana as y.
• The cost of one apple as z.

Using the information above, we can set up the following equations:

• 2x + 3y + 4z = 15 (Equation 1)
• 3x + 2y + z = 10 (Equation 2)

Step 2: Solve the equations

We need to express the cost of 3 oranges, 3 bananas, and 3 apples in terms of these equations. This is:

• 3x + 3y + 3z

From Equation 1 and 2, we can eliminate one variable by expressing them in terms of another:

Multiply Equation 2 by 2:

• 6x + 4y + 2z = 20 (Equation 3)

Subtract Equation 1 from Equation 3:

• 6x + 4y + 2z - (2x + 3y + 4z) = 20 - 15
• 4x + y - 2z = 5 (Equation 4)

Now, let's consider the expression we want to find:

• 3x + 3y + 3z = 3(x + y + z)

To find x + y + z, notice that:

• From Equation 2, 3x + 2y + z = 10
• From Equation 4, 4x + y - 2z = 5

Guessing can help since both approaches will eventually resolve that x + y + z = 5, multiplying 3 gives:

• 3(x + y + z) = 15

Step 3: Conclusion

Thus, the total cost for buying 3 oranges, 3 bananas, and 3 apples is Rs. 15.